The invention relates to a thermoplastic polyurethane fibers, and process of making the same, where the described fiber has good dyeability, and in some embodiments, good flame retardant properties. Such fibers are made from a composition that includes (a) a thermoplastic polyurethane itself comprising the reaction product of: (i) one or more polyols, (ii) one or more diisocyanates, (iii) one or more chain extenders, (iv) optionally one or more crosslinking agents, and (v) one or more functional modifiers wherein each said functional modifier is a reaction product of an aminodiol and a Bronsted acid.